Random numbers are used in a multiplicity of information-technological applications, for example in the context of simulation methods, global optimization methods or local optimization methods, genetic algorithms, etc.
The use of random numbers is of particular importance in the case of cryptographic methods used inter alia for smart cards, security controllers or so-called Trusted Platform Modules (TPM).
The random number sequences that are generated deterministically by a pseudo-random number generator can be completely reconstructed by observation of a certain number of sequence elements.
Whereas so-called pseudo-random number generators based on deterministic mathematical algorithms are often used in the case of the abovementioned information-technological applications such as the simulation methods and the optimization methods or the genetic algorithms, so-called True Random Number Generators (TRNG) are required particularly in cryptography in order to be able to ensure a sufficiently high cryptographic security. A true random number generator is usually based on the observation (measurement) of physical effects, for example the radioactive decay of molecules or atoms.
DE 101 17 362 A1 describes a differential stage having one or a plurality of noisy transistors that generates or generate a so-called Random Telegraph Signal (RTS signal). The generated random telegraph signal has two states, each state of the RTS signal having a known random distribution, i.e. an associated known statistical probability density function, although the random distributions of the two signal states need not be identical.
In accordance with DE 101 17 362 A1, a digitized RTS signal is formed from the analog RTS signal by means of sampling and a binary random number sequence is generated from the sampled values, the sequence elements of said binary random number sequence being stochastically independent under predetermined criteria.
In accordance with DE 101 17 362 A1, the RTS signal is sampled with a temporal sampling interval ΔT that is at least twice as long as the average lifetime of a signal state of the RTS signal. The sampling interval ΔT is thus long enough to ensure the independence of the samples to a sufficient extent.
An imbalance in the number of generated first binary values (“zeros”) and second binary values (“ones”), i.e. clearly a bias, may occur on account of the differences in the average lifetimes of the signal states of the RTS signal.
If the bias is too large, which cannot be exactly predicted in the production of electronic chips and thus of the respective noisy transistors, then a functionality class P2 required for example in W. Killmann and W. Schindler, A proposal for: Functionality classes and evaluation methodology for true (physical) random number generators, Technical Report Version 3.1, Federal Office for Security in Information Technology, Bonn, September 2001, i.e. a quality of the transistors formed that suffices for a minimum cryptographic security, cannot be reliably complied with.
Moreover, the random number rate decreases as the sampling interval ΔT increases.
P. Ruβe, Schaltungsentwurf und Synthese eines adaptiven Prädiktionsfilters sowie eines Algorithmus zur Quantilbildung [Circuit design and synthesis of an adaptive predictive filter and an algorithm for quantile formation], study at the University of Dortmund, September 2002 describes, for a multi-bit generator, an adaptation of the quantile variables used therein.
M. Dichtl and N. Janssen, A high quality physical random number generator, in Eurosmart 2000 Security Conference Proceedings, June 2000 describes the construction and the functioning of a digital postprocessing unit.